AlgebraHardIdentifying a linear function from three table values
Algebra practice question
A student claims that the table below shows values of a linear function f. x | f(x) 0 | 12 4 | 6 10 | 3 Which statement about the table is true?
- A. The values are not consistent with a linear function, because the rate of change from x = 0 to 4 differs from that from x = 4 to 10.Correct
- B. f(x) = 12 − (3/2)x for all x in the table.
- C. f(x) = 12 − (1/2)x for all x in the table.
- D. The rate of change is −3 per unit of x throughout.
Answer: A. The values are not consistent with a linear function, because the rate of change from x = 0 to 4 differs from that from x = 4 to 10.
From 0 to 4 the change is −6 over 4, a rate of −3/2; from 4 to 10 it is −3 over 6, a rate of −1/2. A linear function has one rate, so the table cannot come from one.
Why the other answers are wrong
- B. f(x) = 12 − (3/2)x for all x in the table.
- 12 − (3/2)(10) = −3, not 3.
- C. f(x) = 12 − (1/2)x for all x in the table.
- 12 − (1/2)(4) = 10, not 6.
- D. The rate of change is −3 per unit of x throughout.
- −3 per unit would give f(4) = 0.
More Algebra questions
- Hard
For how many integer values of x is −2 < (x − 5)/3 ≤ 1 true? - Hard
The system 2x + 3y = 6 and 4x + 6y = k has infinitely many solutions. What is the value of k? - Hard
Which of the following is the complete solution set to |x − 4| < 6? - Hard
A student has $40 to spend on notebooks costing $4 each and pens costing $2 each, and wants at least 12 items … - Hard
What is the least whole number of minutes of international calling in a month for which the total monthly cost… - Hard
How many liters of the 30% acid solution did the technician use?
Not affiliated with the College Board. SAT is a trademark of the College Board.